lem:BST-twinwidth implies thm:approx-algo:
to approximate the twin-width of \(T\) , it suffices to compute any BST order in takes polynomial time,
and then apply the approximation algorithm for ordered structures [1]},
which is fixed parameter tractable.
This last algorithm produces either a contraction sequence
(which is valid for \((T,<)\)  and a fortiori for \(T\) ),
or a witness that \((T,<)\)  has large twin-width,
which in turn implies that \(T\)  has large twin-width by lem:BST-twinwidth.
